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Properties

Label 169050.dk
Number of curves $2$
Conductor $169050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dk1")
 
E.isogeny_class()
 

Elliptic curves in class 169050.dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.dk1 169050gj2 \([1, 0, 1, -33101, 10576598]\) \(-2181825073/25039686\) \(-46029594034593750\) \([]\) \(1866240\) \(1.8793\)  
169050.dk2 169050gj1 \([1, 0, 1, 3649, -374902]\) \(2924207/34776\) \(-63927525375000\) \([]\) \(622080\) \(1.3300\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 169050.dk have rank \(0\).

Complex multiplication

The elliptic curves in class 169050.dk do not have complex multiplication.

Modular form 169050.2.a.dk

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} + 5 q^{13} + q^{16} - q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.